Limit theorems of continuous-time random walks with tails

Yuqiang Li

doi:10.1007/s11464-013-0275-0

Limit theorems of continuous-time random walks with tails

Yuqiang Li^*

^*此作品的通讯作者

统计学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M₁-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J₁-topology.

源语言	英语
页（从-至）	371-391
页数	21
期刊	Frontiers of Mathematics in China
卷	8
期	2
DOI	https://doi.org/10.1007/s11464-013-0275-0
出版状态	已出版 - 4月 2013

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10.1007/s11464-013-0275-0

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title = "Limit theorems of continuous-time random walks with tails",

abstract = "We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable L{\'e}vy process in D([0, 1]) with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J1-topology.",

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AB - We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J1-topology.

KW - Weak convergence

KW - stable Lévy process

UR - https://www.scopus.com/pages/publications/84875524466

U2 - 10.1007/s11464-013-0275-0

DO - 10.1007/s11464-013-0275-0

M3 - 文章

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VL - 8

SP - 371

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JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

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Limit theorems of continuous-time random walks with tails

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